Solving proportions is fairly straight forward, but we need to take our time and think about each step so we don't make little mistakes (such as with signs, inverse operations, etc). You've learned and know how to do everything needed to solve proportions and now we just need to put it all together.
Solving proportions (2 ratios/fractions that are EQUAL) is the ONLY time that you will use cross-multiplication. DO NOT use cross multiplying any other time!
What is cross-multiplying?
Cross-multiplying is when you have 2 fractions that are equal and you multiply the numerator of one fraction by the denominator of the other. Then, you set the products equal to each other and solve the resulting equation for the variable. Here's an example:
First, we have to multiply the numerator of each ratio/fraction by the denominator of the other ratio/fraction:
3 times 12 give us 36. 4 times x gives us 4x. Then, we set these two products equal to each other (it DOES NOT matter which side of the equation each product goes on. You will get the same answer either way).
Then, we solve the equation using inverse operations (divide by 4 on both sides of the equation):
TASK: Explain in words how to solve proportions. Be specific.
That's basically all there is to it! We just cross-multiply, set the products equal to each other, and solve the resulting equation. It only gets trickier because the multiplication and equation we have to solve get trickier. Here's an example of one that's a bit more difficult:
When cross multiply, we have to multiply 3x and -2 and then multiply -4 and (x + 7) as follows:
Then, to get the x's together, we add 4x on both sides and get:
Then, we divide by --2 on both sides and get our answer:
TASK: Solve the proportions that you set up in the previous lesson. The problems that you used before are copied below.
Solving proportions (2 ratios/fractions that are EQUAL) is the ONLY time that you will use cross-multiplication. DO NOT use cross multiplying any other time!
What is cross-multiplying?
Cross-multiplying is when you have 2 fractions that are equal and you multiply the numerator of one fraction by the denominator of the other. Then, you set the products equal to each other and solve the resulting equation for the variable. Here's an example:
First, we have to multiply the numerator of each ratio/fraction by the denominator of the other ratio/fraction:
3 times 12 give us 36. 4 times x gives us 4x. Then, we set these two products equal to each other (it DOES NOT matter which side of the equation each product goes on. You will get the same answer either way).
Then, we solve the equation using inverse operations (divide by 4 on both sides of the equation):
TASK: Explain in words how to solve proportions. Be specific.
That's basically all there is to it! We just cross-multiply, set the products equal to each other, and solve the resulting equation. It only gets trickier because the multiplication and equation we have to solve get trickier. Here's an example of one that's a bit more difficult:
When cross multiply, we have to multiply 3x and -2 and then multiply -4 and (x + 7) as follows:
Then, to get the x's together, we add 4x on both sides and get:
Then, we divide by --2 on both sides and get our answer:
TASK: Solve the proportions that you set up in the previous lesson. The problems that you used before are copied below.
1.
2.
3.